Question: Multiply the following complex numbers: $({-i}) \cdot ({-1+4i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-i}) \cdot ({-1+4i}) = $ $ ({0} \cdot {-1}) + ({0} \cdot {4}i) + ({-1}i \cdot {-1}) + ({-1}i \cdot {4}i) $ Then simplify the terms: $ (0) + (0i) + (1i) + (-4 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 0 + (0 + 1)i - 4i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 0 + (0 + 1)i - (-4) $ The result is simplified: $ (0 + 4) + (1i) = 4+i $